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Spotless dice

Upon Amie Albrecht and Cathy Wilton's request, I am writing a blog post about a problem we worked on at One Hundred Factorial recently. A few weeks ago we became interested in problems involving removing spots from dice.

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The right order for the fundamental trig identity

If you google "fundamental trig identity" you will get many many images and handouts which all list the fundamental trig identity as:

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